In this paper we continue the analysis of new non-relativistic string when
we focus on its explicit formulation as non-relativistic limit of \(AdS_5\times S^5\)  background. Our starting point is an important paper [1]}
where non-relativistic strings in \(AdS_5\times S^5\)  was defined by specific limiting procedure. We combine this procedure with the definition of Newton-Cartan fields as was given in [2]} and we will be able
to find Newton-Cartan background fields for non-relativistic limit of \(AdS_5\times S^5\) . Explicitly, we find \(2\times 2\)  twobein \(\tau _M^{ \ A}\)  together with field \(\pi _M^{ \ A}\)  that was introduced in
[2]}. Then we will be able to determine two form \(m_{MN}\)  and hence corresponding Hamiltonian. As the next step we study gauge fixed form of the theory when we impose uniform light-cone gauge. Solving Hamiltonian constraint we determine Hamiltonian on the reduced phase space. We find that the structure of this Hamiltonian depends on the
free parameter that defines generalized uniform light cone gauge [4]}, [5]}, [6]}, [7]}. Then we study equations of motion on the reduced phase space. We show that it is possible to have configuration with all free fields to be equal to zero and concentrate on the dynamics of the mode \(z_1\) . However then we find that the equation of motion for \(z_1\)  is solved by arbitrary function and hence does not determine dynamics of \(z_1\)  at all. We mean that this is a sign that the present form of uniform light cone gauge is not suitable for the specific form of non-relativistic string studied in this paper.
